Daily Prep 11B -- MTH 201-04

--- tags: mth201, dailyprep --- # Daily Prep 11B -- MTH 201-04 ## Overview We've spent the entire course studying one of two things: *derivatives* which tell us rates of change, and *integrals* which tell us total change. In Module 11B, and continuing into Module 12, our last concept of the course is a major mathematical fact that ties these two ideas together. It's called the **Fundamental Theorem of Calculus** (FTC). The FTC unifies the integral and the derivative, and as a by-product it gives a way to compute definite integrals without geometry and without approximation. ## Learning objectives **Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. + State the Fundamental Theorem of Calculus. + Use the Fundamental Theorem of Calculus to find the exact value of a definite integral using an antiderivative. **Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. + Use the Fundamental Theorem of Calculus to find the exact value of a definite integral using an antiderivative (for more complex functions). ## Resources for learning Watch these at the GVSUMath YouTube playlist: - Screencast 4.4.1 -- Quick review: The Fundamental Theorem of Calculus (3:15) https://www.youtube.com/watch?v=bwjUioJyWe8&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=88 - Screencast 4.4.2 -- Fundamental Theorem of Calculus with power functions (7:33) https://www.youtube.com/watch?v=1uxPq8Gtm18&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=89 - Screencast 4.4.3 -- Fundamental Theorem of Calculus with exponential functions (7:57) https://www.youtube.com/watch?v=SafcRvQKe4g&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=90 **Text:** In the _Active Calculus_ text, read Section 4.4 up to but not including subsection 4.4.3 ("The total change theorem") and then stop. (Module 12 will pick up with the total change theorem.) ## Exercises The exercises for this Daily Prep are found on student.desmos.com ("MTH 201 Daily Prep 11B"). ## Submission and grading **Submitting your work:** Just work through the activities; your work is saved as you go. **How this is graded:** Daily Prep assignments are graded on the basis of *completeness and effort*: If your submission has **all parts completed** (no blank entries, even if left blank accidentally) and **a good-faith effort to provide a correct solution or explanation is given** (no responses of "I don't know" or "I didn't understand") and **the work is submitted on time**, it gets a "check". Otherwise it gets an "x". If you are stuck on an item, you're expected to ask questions and give your best effort.